Wind turbine control method using an estimation of the incident wind speed

ABSTRACT

The invention is a method for controlling a wind turbine to optimize the energy production in which control was an estimation of the incident wind speed V w  to obtain an optimum control (COM) θ sp ,T e   sp . The estimation of wind speed V w  is achieved by accounting for the dynamics of the system (MOD DYN) from the measurement of rotor speed Ω r  the torque imposed on the generator T e  and of orientation θ of the turbine blades.

CROSS REFERENCE TO RELATED APPLICATIONS

Reference is made to French Application Serial No. 12/02.601, filed on Oct. 1, 2012 and PCT/FR2013,052040, filed on Sep. 4, 2013, which applications are incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to renewable energy and more particularly to control of wind turbines.

2. Description of the Prior Art

A wind turbine allows the kinetic energy from the wind to be converted into electrical or mechanical energy. For conversion of the wind energy to electrical energy, the wind turbine is made up of the following elements:

-   -   A tower allowing a rotor to be positioned at a sufficient height         to enable motion thereof (necessary for horizontal-axis wind         turbines) or allowing the rotor to be positioned at a height         enabling it to be driven by a stronger and more regular wind         than at ground level. The tower generally houses part of the         electric and electronic components (modulator, control,         multiplier, generator, etc.).     -   A nacelle mounted at the top of the tower, housing mechanical,         pneumatic and some electric and electronic components necessary         to operate the machine. The nacelle can rotate to adjust the         machine to the correct wind direction;     -   A rotor fastened to the nacelle, comprising blades (generally         three) and the nose of the wind turbine. The rotor is driven by         wind energy and it is connected by a mechanical shaft, directly         or indirectly (via a gearbox and mechanical shaft system), to an         electric machine (electric generator) that converts the energy         recovered to electrical energy and     -   A transmission having two shafts (mechanical shaft of the rotor         and mechanical shaft of the electric machine) connected by a         transmission (gearbox).

Since the beginning of the 1990s, there has been renewed interest in wind power, in particular in the European Union where the annual growth rate is about 20%. This growth is attributed to the benefit of carbon-emission-free electricity generation. In order to sustain this growth, the energy yield of wind turbines still has to be improved. The prospect of wind power production increase requires developing effective production tools and advanced control tools in order to improve the performance of the machines. Wind turbines are designed to produce electricity at the lowest possible cost. They are therefore generally built to reach their maximum performance at a wind speed of approximately 15 m/s. It is in fact unnecessary to design wind turbines that maximize their yield at higher wind speeds, which are not common. In the case of wind speeds above 15 m/s, it is necessary to not capture part of the additional energy contained in the wind to avoid damage to the wind turbine. All wind turbines are therefore designed with a power regulation system.

For this power regulation, controllers have been designed for variable-speed wind turbines. The purpose of the controllers is to maximize the electrical power which is recovered, to minimize the rotor speed fluctuations and to minimize the fatigue and the extreme moments of the structure (blades, tower and platform).

Linear controllers have been widely used for power control which control the blade pitch angle (orientation of the blades). These include techniques using PI (proportional integral) and PID (proportional integral derivative) controllers, LQ (linear quadratic) control techniques and strategies based on robust linear controls.

However, the performance of these linear controllers is limited by the highly non-linear characteristics of the wind turbine. First strategies based on non-linear controls have been developed, such a strategy is for example described in the document: Boukhezzar B., Lupu L., Siguerdidjane H., Hand M. “Multivariable Control Strategy for Variable Speed, Variable Pitch Wind Turbines” Renewable Energy, 32 (2007) 1273-1287.

None of these strategies however uses the incident wind speed, which is a fundamental element for the aerodynamic phenomena that govern the wind turbine. To take this component into account, initial work was performed with a measurement of the wind speed. This work shows that the productivity of a wind turbine and the life thereof can be significantly increased through innovative strategies using the wind speed.

This technique unfortunately requires a sensor that is expensive and not very accurate. To take the incident wind speed into account without a sensor, an estimation of this speed can be performed to use this data in the control. Further work has been conducted to this end using a Kalman filter, which is described in the document: Boukhezzar B., Siguerdidjane H., “Nonlinear Control of Variable Speed Wind Turbine Without Wind Speed Measurement” IEEE Control and Decision Conference (2005). This method is not sufficiently accurate because the wind reconstruction is poorly representative. Indeed, according to this method, the wind is not structured, it is considered as white noise, which is not the case experimentally.

SUMMARY OF THE INVENTION

The invention relates to a method for controlling a wind turbine in order to optimize the energy produced with control accounting for an estimation of the incident wind speed. Estimation of the wind speed is achieved by accounting for the dynamics of the system, from the measurement of the rotor speed, the torque imposed on the generator and of the orientation of the turbine blades for an accurate estimation.

The invention relates to a method for controlling a wind turbine including a rotor to which at least one blade is attached, and an electric machine connected to the rotor, wherein a pitch angle θ of the at least one blade and an electrical recovery torque T_(e) of the electric machine are known. The method comprises carrying out the following stages:

-   -   a) constructing a dynamic model of the rotor by applying the         fundamental principle of dynamics to the rotor wherein the model         relates the incident wind speed at the wind turbine V_(w) to a         rotating speed of the rotor Ω_(r) , to the pitch angle θ of the         blade and to the electrical recovery torque T_(e);     -   b) measuring the rotating speed of the rotor Ω_(r);     -   c) determining the incident wind speed V_(w) from use of the         rotor dynamics model, of the measured rotating speed of the         rotor Ω_(r), of the pitch angle θ of the blade and of the         electrical torque T_(e); and     -   d) controlling the pitch angle θ of the blade and/or the         electrical recovery torque T_(e) as a function of the incident         wind speed V_(w) to optimize the production of energy by said         wind turbine.

According to the invention, the rotor dynamics model is expressed by the relationship:

${{J_{r}\frac{\Omega_{r}}{t}} = {T_{aero} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e}}},$

with J_(r) being the inertia of the rotor, T_(aero) being the aerodynamic torque applied to the rotor that depends on the incident wind speed V_(w) , the rotating speed of the rotor Ω_(r) and the pitch angle θ, T_(l) (Ω_(r)) being friction and load torque on the rotor that depends on the rotating speed of the rotor Ω_(r), and N being the transmission ratio between the rotor and the electric machine.

Advantageously, the aerodynamic torque applied to the rotor is expressed by a formula:

${T_{aero} = {0.5\; {\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}V_{w}^{2}}},$

with R_(b) being the radius of the rotor, ρ being the air density, c_(q) being a parameter determined by mapping the rotor as a function of the pitch angle θ and of ratio

$\frac{R_{b}\Omega_{r}}{V_{w}}.$

According to an embodiment of the invention, when the incident wind speed V_(w) is considered as a harmonic perturbation, the incident wind speed V_(w) can be written with a formula:

${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({{\omega}_{k}t})}}}$

with p being the number of harmonics considered, ω_(k) being the frequency of harmonic k, c_(k) being the coefficient of harmonic k, and the incident wind speed V_(w) is determined by determining parameters ω_(k) and c_(k) by use of the rotor dynamics model, then the incident wind speed is deduced therefrom.

Preferably, the frequency of a harmonic k is determined using a formula of the type:

$\omega_{k} = {3{\frac{k}{p}.}}$

Advantageously, coefficients c_(k) are determined by solving a system of equations of the form:

$\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5\; {\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$

with L_(Ω) being a gain that controls the convergence rate of the estimation of the rotor rotating speed, L_(k) being a gain that controls the convergence rate of the harmonic decomposition, and Ω representing the measured rotor speed.

Preferably, the gain L_(Ω) is substantially 1 and the gain L_(k) is determined with a formula:

$L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$

Furthermore, the pitch angle θ can be controlled by use of the following stages:

-   -   i) determining an aerodynamic torque setpoint T_(aero) ^(sp) an         electric machine torque setpoint R_(e) ^(sp) which allows         maximizing the power recovery, from the incident wind speed         V_(w), measurements of the rotor rotating speed Ω_(r) and the         rotating speed of the electric machine shaft Ω_(e);     -   ii) modifying at least one of the setpoint values by subtracting         a term proportional to a difference between measured rotor speed         Ω_(r) and measured electric machine speed Ω_(e);     -   iii) determining a pitch angle θ^(sp) for the blade permitting         achieving the aerodynamic torque setpoint R_(aero) ^(sp); and     -   iv) orienting the blade according to the pitch angle θ^(sp).

Preferably, at least one of the setpoint values is modified by carrying out the following stages:

-   -   (1) determining a torque T _(res) on the transmission resulting         from the aerodynamic torque T_(aero) ^(sp) and electric machine         torque T_(e) ^(sp) setpoints;     -   (2) determining a resulting torque setpoint T_(res) _(sp) by         subtracting from the resulting torque T_(res) a term         proportional to the difference between measured rotor speed         Ω_(r) and measured electric machine speed Ω_(e); and     -   (3) modifying the aerodynamic torque setpoint T_(aero) ^(sp) by         distributing the resulting torque setpoint T_(res) _(sp) between         an aerodynamic torque T_(aero) ^(sp) and an electric machine         torque T_(e) ^(sp).

According to an embodiment of the invention, the resulting torque setpoint T_(res) ^(sp) is written as follows: T_(res) ^(sp)= T _(res)−k{dot over (γ)}_(tr) with k being strictly positive calibration parameters and {dot over (γ)}_(tr) being speed of a gear transmission torsion, equal to a difference of rotor speed Ω_(r) and electric machine speed Ω_(e) brought into the same axis:

${{\overset{.}{\gamma}}_{tr} = {\Omega_{r} - {\frac{1}{N}\Omega_{e}}}},$

where N is a gear ratio between the rotor and the electric machine.

Furthermore, the pitch angle of the blade can be determined by inverting an aerodynamic torque model and using the incident wind speed V_(w) and measured rotor speed Ω_(r).

Advantageously, the proportional term is determined using a transmission dynamics model.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the method according to the invention will be clear from reading the description hereafter of embodiments given by way of non limitative example, with reference to the accompanying figures wherein:

FIG. 1 illustrates the stages of the method according to the invention;

FIG. 2 illustrates the stages of the method according to an embodiment of the invention;

FIG. 3 shows a map of the rotor giving coefficient c_(q) as a function of pitch angle θ and of ratio

$\frac{R_{b}\Omega_{r}}{V_{w}};$

and

FIG. 4 illustrates the wind turbine control stages according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The invention relates to a method for controlling an onshore or offshore horizontal-axis wind turbine, wherein the pitch angle of the blades and/or the electrical recovery torque of the electric machine are controlled to optimize energy recovery.

Notations

In the description hereafter, the following notations are used:

-   -   θ is the pitch angle of the blades which is the angle between         the blades and a reference such as the ground (horizontal plane,         perpendicular to the tower of the wind turbine) and the pitch         angle can be controlled by the method according to the         invention;     -   T_(e) is the electrical recovery torque of the electric machine,         which can be controlled by the method according to the         invention;     -   V_(w) is the incident wind speed at the blades of the wind         turbine which is estimated by the method according to the         invention;     -   Ω_(r) is the rotating speed of the wind turbine rotor which can         be measured;     -   Ω_(e) is the rotating speed of the electric machine shaft which         can be measured;     -   J_(r) is the inertia of the wind turbine rotor which is a known         value;     -   J_(g) is the inertia of the electric machine;     -   T_(aero) is the aerodynamic torque applied to the rotor which is         the rotational force applied to the rotor under the effect of         wind;     -   T_(l) is the friction and load torque on the rotor which can be         determined by a second-order polynomial of the rotor rotating         speed Ω_(r);     -   N is the gear ratio between the rotor and the electric machine;     -   R_(b) is the rotor radius;     -   ρ is the air density. The density varies as a function of         temperature and atmospheric pressure. It is generally around 1.2         kg/m³;     -   c_(q) is the coefficient given by a map of the rotor as a         function of pitch angle θ and ratio

$\frac{R_{b}\Omega_{r}}{V_{w}}$

FIG. 3 is an example of a map used for determining the coefficient;

-   -   c_(k) is the coefficient of harmonic k of the harmonic         decomposition of incident wind speed V_(w);     -   ω_(k) is the frequency of harmonic k of the harmonic         decomposition of incident wind speed V_(w);     -   p is the number of harmonics considered for the harmonic         decomposition of incident wind speed V_(w);     -   L_(Ω) is the gain controlling the convergence rate of the rotor         speed estimation;     -   L_(k) is the gain controlling the convergence rate of the         harmonic decomposition of incident wind speed V_(w);     -   T_(res) is the resulting torque on the transmission between the         rotor and the electric machine;     -   {dot over (γ)}_(tr) is the torsion speed of the transmission         between the rotor and the electric machine.

These notations, when followed by superscript -^(sp), represent the setpoints associated with the quantities considered.

FIG. 1 shows the method according to the invention. The stages of the method according to the invention are as follows:

-   -   1) Measurement of rotor rotating speed Ω_(r)     -   2) Construction of a rotor dynamics model (MOD DYN)     -   3) Wind turbine control (COM)

Stage 1)—Measurement of the Rotor Rotating Speed

Rotor rotating speed Ω_(r) is measured during operation of the wind turbine, notably by a rotation sensor.

Stage 2)—Construction of a Rotor Dynamics Model (MOD DYN)

The actual pitch angle θ of the blades is first determined, as well as electrical recovery torque T_(e) , by measuring (with a sensor for example) or as a function of the control applied to the actuators to modify these parameters.

A rotor dynamics model is then constructed. A rotor dynamics model is understood to be a model representing the dynamic phenomena applied to the rotor. This model is obtained by applying the fundamental principle of dynamics to the rotor. The model allows relating the incident wind speed V_(w) to a rotating speed of the rotor Ω_(r), to pitch angle θ of the blade and to electrical recovery torque T_(e) of the electric machine.

This rotor dynamics model is then applied with known data: θ and T_(e), and at the measured value Ω_(r), which thus allows to determine incident wind speed V_(w).

FIG. 2 shows an embodiment of the method according to the invention. For this embodiment, the rotor dynamics model (MOD DYN) is constructed by use of a model of the aerodynamic torque (MOD AERO), of the fundamental dynamics principle (PFD) applied to the rotor and of a wind model (MOD VENT).

Aerodynamic Torque Model (MOD AERO)

According to this embodiment of the invention, aerodynamic torque T_(aero) is modelled by a model describing the wind power contained in a cylinder, multiplied by a factor describing the fact that a wind turbine only allows recovery of part of this power. Aerodynamic torque T_(aero) is thus modelled as a function of incident wind speed V_(w) pitch angle θ and rotor speed Ω_(r). Such a model can be expressed under steady state conditions as

$T_{aero} = {0.5\; {\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}{V_{w}^{2}.}}$

The parameter c_(q) can be determined by mapping the rotor. An example of mapping parameter c_(q) is shown in FIG. 3. This map shows the value of parameter c_(q) as a function of ratio

$\frac{R_{b}\Omega_{r}}{V_{w}}$

for various pitch angles (a curve for each θ). This type of map is well known. Ratio

$\frac{R_{b}\Omega_{r}}{V_{w}}$

is denoted by TSR in FIG. 3.

Aerodynamic torque T_(aero) can therefore be written as a function of quantities related to the wind turbine (ρ,R_(b)), of the known value (θ) and of the incident wind speed to be estimated (V_(w)).

Fundamental Dynamics Principle (PFD)

By writing the fundamental dynamics principle applied to the rotor concerning the moments on the axis of rotation thereof, a relation is obtained of the type:

${J_{r}\frac{\Omega_{r}}{t}} = {T_{aero} - {T_{l}\left( \Omega_{r} \right)} - {{NT}_{e}.}}$

In this relation, the aerodynamic torque T_(aero) determined with the aerodynamic torque model described above is used. Furthermore, the friction and load torque on the rotor T_(l) can be conventionally determined by a second-order polynomial of rotating speed Ω_(r) of the rotor.

By combining the two models, a relation between incident wind speed V_(w) and the known or measured quantities such as pitch angle θ of the blades, electrical recovery torque T_(e) and rotating speed Ω_(r) of the rotor can be established.

Incident Wind Modelling (MOD VENT)

The last modelling stage considers the wind as a harmonic perturbation. This means an assumption that the wind can be is written in the form:

${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}}$

with p being the number of harmonics considered for the harmonic decomposition of the wind, p=50 can be selected for example.

Moreover, for the frequency of the harmonics,

$\omega_{k} = {3\frac{k}{p}}$

in Hz (with k>0) can be chosen.

By combining the three models presented above, a dynamic model of the form as follows can be obtained:

$\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {0.5\; \rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}} \right)^{2}}} & {{- {T_{l}\left( \Omega_{r} \right)}} - {NT}_{e}} \\ {\frac{c_{k}}{t} = 0} & {{{for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack} \end{matrix} \right.$

From this system of equations, an observer can be constructed allowing determination of coefficients c_(k) of the harmonic decomposition of the incident wind. The observer can be written in the form:

$\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {0.5\; \rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}\; {c_{k}^{({\; \omega_{k}t})}}} \right)^{2}}} & {{- {T_{l}\left( \Omega_{r} \right)}} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}} \\ {\frac{c_{k}}{t} = {{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}}} & {{{for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack} \end{matrix} \right.$

where Ω represents the measured rotor speed, L_(Ω) is necessarily a positive gain controlling the convergence rate of the rotor speed estimation. The gain can be selected equal to 1 for example, and {L_(k)}_(k∈[−p,p]) is a gain controlling the convergence rate of the harmonic decomposition. These gains must be positive, and can be selected equal to

$\frac{10}{1 + \omega_{k}^{2}}$

for example.

The latter system of equations represents an adaptive type non-linear estimator allowing estimation of coefficients c_(k) of the harmonic decomposition of the incident wind signal V_(w).

This method reconstructs the excitation of wind V_(w) through coefficients c_(k) . Reconstructed wind V_(w) is given by the relation as follows:

${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}\; {c_{k}{^{({{\omega}_{k}t})}.}}}$

Stage 3)—Wind Turbine Control (COM)

Depending on incident wind speed V_(w), the wind turbine is controlled so as to optimize the energy recovered. According to the invention, pitch angle θ of the blades and/or electrical recovery torque T_(e) can be controlled as a function of incident wind V_(w).

According to an embodiment of the invention, pitch angle θ of the blades and/or electrical recovery torque T_(e) are determined by mapping the wind turbine as a function of incident wind V_(w).

Alternatively, according to an embodiment of the invention illustrated in FIG. 4, pitch angle θ of the blades can be controlled by the following stages:

-   -   1—Determining the pitch allowing the recovered power to be         optimized         -   i—Generating an electrical torque setpoint T_(e) ^(sp)         -   ii—Generating an aerodynamic torque setpoint T_(aero) ^(sp)         -   iii—Determining a pitch position θ     -   2—Determining the torque resulting from the torque setpoints         T_(e) _(sp) and T_(aero) ^(sp)     -   3—Generating a resulting torque setpoint (T_(res) ^(sp)) that         decreases fatigue and extreme moments of the transmission     -   4—Distributing the resulting torque setpoint (T_(res) ^(sp))         between the aerodynamic and electrical torques     -   5—Determining a pitch position allowing this aerodynamic torque         to be achieved     -   6—Orienting the blades at the determined pitch angle.

1—Determining the Pitch Allowing the Recovered Power to be Optimized

One goal of the method according to the invention is to maximize the energy production of an onshore or offshore horizontal-axis wind turbine (blade perpendicular to the wind) while limiting extreme moments and fatigue of the mechanical structure.

To maximize the energy production of a wind turbine, the pitch angle θ of the blades allowing maximizing the recovered power P_(aero) as a function of incident wind speed V_(w) determined in the rotor dynamics model construction stage is sought.

According to an embodiment, a model of the recoverable power is used to define this angle. This power P_(aero) can be written as follows:

P _(aero) =T _(aero)*Ω_(r)

Angle θ allowing P_(aero) to be maximized is thus sought. The following stages are therefore carried out:

-   -   i—Generating an electric machine torque setpoint T_(e) ^(sp)     -   ii—Generating an aerodynamic torque setpoint T_(aero) ^(sp)     -   iii—Determining a pitch position θ

i—Generating an Electric Machine Torque Setpoint T_(e) ^(sp)

An electric machine torque setpoint T_(e) ^(sp) is first determined. This setpoint value is obtained through mapping as a function of the speed of the electric machine.

According to the invention, aerodynamic torque T_(aero) is modelled by the aerodynamic model as described in the dynamic model construction part.

$T_{aero} = {0.5\; {\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}V_{w}^{2}}$

Thus, to determine the torque setpoint for the electric machine as a function of the speed of the electric machine, the aerodynamic power recovered for each wind speed is optimized.

$T_{e}^{sp} = {\arg \left( {\max_{\theta,V_{w}}{\frac{0.5}{N}\rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{g}}{{NV}_{w}}} \right)}V_{w}^{2}}} \right)}$

This allows having torque setpoint T_(e) that depends on the rotating speed of the electric machine shaft: T_(e) ^(sp)=f(Ω_(e)).

However, in relation to this reference curve, two limitations are applied:

-   -   a zero torque for low electric machine speeds so that the wind         turbine speed can be increased     -   a maximum torque to limit the power of the electric machine.

Thus, there are three regions in the curve T_(e) ^(sp)=f(Ω_(e)):

-   -   Region 1: zero torque     -   Region 2: optimum torque     -   Region 3: torque limited by the maximum power.

ii—Generating an Aerodynamic Torque Setpoint T_(aero) ^(sp)

The purpose is to generate an aerodynamic torque setpoint T_(aero) ^(sp) allowing achieving the rotor rotating speed setpoint Ω_(r) ^(sp). The rotor dynamics model is therefore used.

${J_{r}\frac{\Omega_{r}}{t}} = {T_{aero} - {T_{l}\left( \Omega_{r} \right)} - {{NT}_{e}\left( \Omega_{e} \right)}}$

Thus, the control strategy used is a dynamic control strategy that anticipates the setpoint variation and corrects with two terms which are a proportional term and an integral term. The strategy is written with a relation of the form:

$T_{aero}^{sp} = {{T_{l}\left( \Omega_{r} \right)} + {{NT}_{e}\left( \Omega_{r} \right)} + {J_{r}\frac{\Omega_{r}^{sp}}{t}} - {k_{p}\left( {\Omega_{r} - \Omega_{r}^{sp}} \right)} - {k_{i}{\int\left( {\Omega_{r} - \Omega_{r}^{sp}} \right)}}}$

where kp and ki are two real parameters to be calibrated so as to guarantee convergence of the speed to the setpoint thereof.

iii—Determining a pitch position θ

From this aerodynamic torque setpoint T_(aero) ^(sp), a pitch angle θ is determined for the blades to satisfy this aerodynamic torque request T_(aero) ^(sp). The aerodynamic torque model is therefore used with the incident wind speed V_(w) determined in the rotor dynamics model construction stage, the measured rotor speed Ω_(r) ^(sp) and the torque setpoint T_(aero) ^(sp). By inverting the model (using a Newton algorithm for example), a pitch setpoint θ is obtained:

$\overset{\_}{\theta} = {\arg \left( {\min_{\theta}\left( {T_{aero}^{sp} - {0.5\; \rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}V_{w}^{2}}} \right)^{2}} \right)}$

Thus, with this control law, the convergence to the reference rotor speed allowing the recovered power to be maximized is guaranteed.

2—Determining the Torque Resulting from the Torque Setpoints T_(e) ^(sp) and T_(aero) ^(sp)

From setpoints T_(e) ^(sp) and T_(aero) ^(sp), torque T _(res) resulting from these two torques and relating to the transmission is determined. Therefore, this torque is modeled by us of the formula as follows:

${\overset{\_}{T}}_{res} = {{\frac{J_{g}}{J_{r} + J_{g}}\left( {T_{aero}^{sp} - T_{l}} \right)} + {\frac{J_{r}}{J_{r} + J_{g}}{NT}_{e}^{sp}}}$

where J_(r) and J_(g) are the inertias of the rotor and of the electric machine respectively.

3—Generating a Resulting Torque Setpoint (T_(res) ^(sp)) that Decreases the Fatigue and the Moments of the Transmission

It is desired to modify this resulting torque T _(res) in order to minimize the impact on the transmission and thus to increase the life thereof. Therefore, it is desirable to decrease the torsion speed variations of the transmission. Thus, an attempt is made to compensate for the torque with terms proportional to the difference between the speed of the rotor and of the electric machine. The dynamics of the mechanical structure (transmission dynamics) can be written in form of two coupled second-order systems.

$\left\{ {\begin{matrix} {{\frac{J_{r}J_{g}}{J_{r} + J_{g}}{\overset{¨}{\gamma}}_{tr}} = {{{- c_{d}}\gamma_{tr}} - {k_{d}{\overset{.}{\gamma}}_{tr}} + {\frac{J_{g}}{J_{r} + J_{g}}\left( {T_{aero} - T_{l}} \right)} + {\frac{J_{r}}{J_{r} + J_{g}}{NT}_{e}}}} \\ {{J_{g}{\overset{.}{\Omega}}_{e}} = {{c_{d}\gamma_{tr}} + {k_{d}{\overset{.}{\gamma}}_{tr}} + {N_{gb}T_{e}}}} \end{matrix}\quad} \right.$

where:

-   -   γ_(tr), {dot over (γ)}_(tr) and {umlaut over (γ)}_(tr) are the         angle, the speed and the acceleration of the torsion of the         shaft respectively. It should be noted that the transmission         torsion speed is the difference between the speed of the rotor         and the generator brought into the same axis, that is

${\overset{.}{\gamma}}_{tr} = {\Omega_{r} - {\frac{1}{N}\Omega_{e}}}$

-   -   k_(d) is the structural transmission damping     -   c_(d) is the transmission stiffness     -   N_(gb) is the gearbox ratio, that is the ratio of the generator         speed to the rotor speed.

Thus, the control strategy is designed to generate a resulting torque different from T _(res) to minimize the fatigue and the extreme moments of the transmission. Accordingly, the relationship is obtained:

T _(res) ^(sp) =T _(res) −k{dot over (γ)} _(tr)

with k being strictly positive calibration parameters. These parameters can be determined experimentally. All the parameters k can be considered equal to 1 for example.

4—Distributing the Resulting Torque Setpoint (T_(res) ^(sp)) Between the Aerodynamic and Electrical Torques

This resulting torque setpoint T_(res) ^(sp) is then distributed between aerodynamic torque T_(aero) and torque T_(e) of the electric machine. Distribution is achieved according to the operating zones. In a zone 2, where the aerodynamic torque is limiting, a torque reserve exists. In this case, the torque modification influences the torque of the electric machine and not the aerodynamic torque.

Thus, in this case, the relationship:

$\left\{ {\begin{matrix} {T_{aero}^{strat} = T_{aero}^{sp}} \\ {T_{e}^{strat} = {T_{e}^{sp} - {k\frac{J_{r} + J_{g}}{{NJ}_{r}}{\overset{.}{\gamma}}_{tr}}}} \end{matrix}\quad} \right.$

Similarly, in a zone 3 where the torque of the electric machine is limiting, the torque modification influences the aerodynamic torque. Therefore, the relationship is obtained:

$\left\{ {\begin{matrix} {T_{aero}^{strat} = {T_{aero}^{sp} - {k\frac{J_{r} + J_{g}}{J_{g}}{\overset{.}{\gamma}}_{tr}}}} \\ {T_{e}^{strat} = T_{e}^{sp}} \end{matrix}\quad} \right.$

5—Determining a Pitch Position Allowing this Aerodynamic Torque to be Achieved

From this aerodynamic torque setpoint T_(aero) ^(strat), a pitch angle θ for the blades to satisfy this aerodynamic torque request T_(aero) ^(strat). Therefore, the aerodynamic torque model with the incident wind speed V_(w) determined in the rotor dynamics model construction stage, the measured rotor speed Ω_(r) ^(sp) and the torque setpoint T_(aero) ^(strat) is used. By inverting the model (using a Newton algorithm for example), a pitch setpoint θ is obtained:

$\overset{\_}{\theta} = {\arg \left( {\min_{\theta}\left( {T_{aero}^{strat} - {0.5\; \rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}V_{w}^{2}}} \right)^{2}} \right)}$

Thus, with this control law, the convergence to the reference rotor speed allowing the recovered power to be maximized, while minimizing the mechanical impact (fatigue and extreme moment) on the transmission is guaranteed.

6—Orienting the Blades at the Determined Pitch Angle

To optimize the electric power recovered by the wind turbine, the blades are oriented at the pitch angle calculated in the previous stage. 

1-12. (canceled)
 13. A method for controlling a wind turbine, comprising a rotor to which at least one blade is attached and an electric machine connected to the rotor, wherein a pitch angle of the at least one blade and an electrical recovery torque of the electric machine are known, comprising: a) constructing a model of dynamics of the rotor using a fundamental principle of dynamics to describe the rotor, the model relating incident wind speed at the wind turbine to a rotating speed of the rotor, to the pitch angle of the blade and to the electrical recovery torque; b) measuring the rotating speed of said rotor; c) determining an incident wind speed by using the model of dynamics of the rotor, of the measured rotating speed of the rotor, of the pitch angle of the at least one blade and of the electrical torque; and d) controlling the pitch angle of the blade and/or the electrical recovery torque as a function of the incident wind speed to optimize production of energy by the wind turbine.
 14. A method as claimed in claim 13, wherein the model of dynamics of the rotor is expressed as: ${{J_{r}\frac{\Omega_{r}}{t}} = {T_{aero} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e}}},$ with J_(r) being inertia of the rotor, T_(aero) being aerodynamic torque applied to the rotor depending on the incident wind speed V_(w), Ω_(r) being the rotating speed of the rotor and the pitch angle θ, T_(l)(Ω_(r)) being the friction and load torque on the rotor depending on the rotating speed of the rotor Ω_(r), and N being a transmission ratio between the rotor and the electric machine.
 15. A method as claimed in claim 14, wherein the aerodynamic torque applied to the rotor is expressed by the relationship: ${T_{aero} = {0.5\; \rho \; \Pi \; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{V_{w}}} \right)}V_{w}^{2}}},$ with R_(b) being the radius of the rotor, ρ being the air density, c_(q) being is a parameter determined by mapping the rotor as a function of the pitch angle θ and of ratio $\frac{R_{b}\Omega_{r}}{V_{w}}.$
 16. A method as claimed in claim 13 wherein, the incident wind speed V_(w) is considered to be a harmonic perturbation, and is expressed by the relationship: ${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}}$ with p being a number of harmonics, ω_(k) being a frequency of harmonic k, c_(k) being a coefficient of harmonic k, and the incident wind speed V_(w) is determined by determining parameters ω_(k) and c_(k) by use of the model of rotor dynamics with the incident wind speed V_(w) being deduced therefrom.
 17. A method as claimed in claim 14 wherein, the incident wind speed V_(w) is considered to be a harmonic perturbation, and is expressed by the relationship: ${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}}$ with p being a number of harmonics, ω_(k) being a frequency of harmonic k, c_(k) being a coefficient of harmonic k, and the incident wind speed V_(w) is determined by determining parameters ω_(k) and c_(k) by use of the model of rotor dynamics with the incident wind speed V_(w) being deduced therefrom.
 18. A method as claimed in claim 15 wherein, the incident wind speed V_(w) is considered to be a harmonic perturbation, and is expressed by the relationship: ${V_{w}(t)} = {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}}$ with p being a number of harmonics, ω^(k) being a frequency of harmonic k, c_(k) being a coefficient of harmonic k, and the incident wind speed V_(w) is determined by determining parameters ω_(k) and c_(k) by use of the model of rotor dynamics with the incident wind speed V_(w) being deduced therefrom.
 19. A method as claimed in claim 16, wherein the frequency of harmonic k is determined by a relationship: $\omega_{k} = {3{\frac{k}{p}.}}$
 20. A method as claimed in claim 17, wherein the frequency of harmonic k is determined by a relationship: $\omega_{k} = {3{\frac{k}{p}.}}$
 21. A method as claimed in claim 18, wherein the frequency of harmonic k is determined by a relationship: $\omega_{k} = {3{\frac{k}{p}.}}$
 22. A method as claimed in claim 16, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L₁₀₆ being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 23. A method as claimed in claim 17, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L_(Ω) being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 24. A method as claimed in claim 18, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L_(Ω) being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 25. A method as claimed in claim 19, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L_(Ω) being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 26. A method as claimed in claim 20, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L_(Ω) being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 27. A method as claimed in claim 21, wherein the coefficient c_(k) is determined by solving a system of equations expressed as: $\quad\left\{ \begin{matrix} {{J_{r}\frac{\Omega_{r}}{t}} = {{0.5{\rho\Pi}\; R_{b}^{3}{c_{q}\left( {\theta,\frac{R_{b}\Omega_{r}}{\sum\limits_{k = {- p}}^{p}{c_{k}^{({{\omega}_{k}t})}}}} \right)}\left( {\sum\limits_{k = {- p}}^{p}{c_{k}^{({\; \omega_{k}t})}}} \right)^{2}} - {T_{l}\left( \Omega_{r} \right)} - {NT}_{e} - {J_{r}{L_{\Omega}\left( {\Omega_{r} - \Omega} \right)}}}} \\ {\frac{c_{k}}{t} = {{{- L_{k}}{^{({{- }\; \omega_{k}t})}\left( {\Omega_{r} - \Omega} \right)}\mspace{14mu} {for}\mspace{14mu} {any}\mspace{14mu} k} \in \left\lbrack {{- p},p} \right\rbrack}} \end{matrix} \right.$ with L_(Ω) being a gain controlling a convergence rate of an estimation of the rotor rotating speed, L_(k) being a gain that controls a convergence rate of harmonic decomposition, and Ω representing a measured rotor speed.
 28. A method as claimed in claim 22, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 29. A method as claimed in claim 23, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 30. A method as claimed in claim 24, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 31. A method as claimed in claim 25, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 32. A method as claimed in claim 26, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 33. A method as claimed in claim 27, wherein the gain L_(Ω) is substantially 1 and the gain L_(k) is determined by a relationship: $L_{k} = {\frac{10}{1 + \omega_{k}^{2}}.}$
 34. A method as claimed in claim 13, wherein the pitch angle θ is controlled by a process comprising: i) determining an aerodynamic torque setpoint and an electric machine torque setpoint allowing maximizing the power recovery, from the incident wind speed, measurements of the rotor rotating speed and the rotating speed of the electric machine shaft; ii) modifying at least one of the setpoint values by subtracting a term proportional to a difference between measured rotor speed and measured electric machine speed; iii) determining a pitch angle for the at least one blade allowing achieving the aerodynamic torque setpoint; and iv) orienting the blade according to the pitch angle.
 35. A method as claimed in claim 34, wherein at least one of the setpoint values is modified by steps comprising: (1) determining a torque on the transmission resulting from the aerodynamic torque and electric machine torque setpoints; (2) determining a resulting torque setpoint by subtracting from the resulting torque a term proportional to a difference between measured rotor speed and measured electric machine speed; and (3) modifying the aerodynamic torque setpoint by distributing the resulting torque setpoint between an aerodynamic torque and an electric machine torque.
 36. A method as claimed in claim 35, wherein the resulting torque setpoint is expressed as: T_(res) ^(sp)= T _(res)−k{dot over (γ)}_(tr) with k being strictly positive calibration parameters and {dot over (γ)}_(tr) being a speed of a gear transmission torsion, equal to a difference of rotor speed Ω_(r) and electric machine speed Ω_(e) brought into a same axis: ${{\overset{.}{\gamma}}_{tr} = {\Omega_{r} - {\frac{1}{N}\Omega_{e}}}},$ where N is a gear ratio between the rotor and the electric machine.
 37. A method as claimed in claim 34, wherein the pitch angle of the at least one blade is determined by inverting an aerodynamic torque model and using the incident wind speed and measured rotor speed.
 38. A method as claimed in claim 34, wherein a proportional term is determined using a model of transmission dynamics. 